in the 74 s after lift-off, the shuttle challenger travels 36 km. assume constant acceleration, calculate
a) the acceleration of the shuttle in m/s^2.
b) the speed of the shuttle in km/h after 74s.
a) d = 1/2 a t^2 ... 36 = 1/2 a 74^2
b) it starts from rest ... so , v = 2 (36 km / 74 s)
... convert km/s to km/hr ... multiply by 3600 s/hr
a) Well, the shuttle sure is a go-getter! To calculate its acceleration in m/s^2, we can use the formula:
acceleration = velocity / time
Since we have the distance (36 km) and time (74 s), we first need to convert the distance to meters:
36 km * 1000 = 36,000 meters
Now, let's plug in the numbers:
acceleration = 36,000 m / 74 s ≈ 486.49 m/s^2
So, the acceleration of the shuttle is approximately 486.49 m/s^2.
b) To find the speed of the shuttle in km/h after 74 seconds, let's use the formula:
speed = acceleration * time
But hold on a minute, we need to convert the acceleration to km/h^2. We can achieve that by multiplying the acceleration by 3.6:
acceleration (km/h^2) = 486.49 m/s^2 * 3.6 = 1753.76 km/h^2
Now, let's find the speed:
speed = 1753.76 km/h^2 * 74 s ≈ 129,698.24 km/h
So, the speed of the shuttle after 74 seconds is approximately 129,698.24 km/h. Let's just hope it didn't pass any speed limits up there!
To solve this problem, we will use the following equations of motion:
1. Velocity (v) = initial velocity (u) + acceleration (a) * time (t)
2. Displacement (s) = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time^2
Given:
Displacement (s) = 36 km = 36,000 m
Time (t) = 74 s
a) To find the acceleration (a), we will use equation (2). Rearranging the equation, we get:
a = (s - u * t) / (0.5 * t^2)
Since we are assuming constant acceleration, the initial velocity (u) can be assumed to be zero for this calculation.
a = (36,000 m - 0 m * 74 s) / (0.5 * (74 s)^2)
a = 36,000 m / (0.5 * 5476 s^2)
a ≈ 13.13 m/s^2
Therefore, the acceleration of the shuttle is approximately 13.13 m/s^2.
b) To find the speed of the shuttle in km/h after 74 s, we will use equation (1). Rearranging the equation, we get:
v = u + a * t
Since the initial velocity (u) is zero, the equation simplifies to:
v = a * t
Converting the time from seconds to hours:
t (hours) = 74 s * (1 min / 60 s) * (1 hr / 60 min)
t (hours) ≈ 0.034722 hr
Substituting the values into the equation:
v = 13.13 m/s^2 * 0.034722 hr * (3600 s / 1 hr) * (1 km / 1000 m)
v ≈ 16.82 km/h
Therefore, the speed of the shuttle after 74 s is approximately 16.82 km/h.
To calculate the acceleration of the shuttle, we can use the formula:
Acceleration (a) = (Change in velocity) / (Change in time)
In this case, the shuttle traveled 36 km in 74 seconds. First, we need to convert the distance traveled from kilometers to meters:
Distance travelled = 36 km = 36,000 m.
Now, we have the values needed to calculate the acceleration:
Change in velocity = Distance travelled = 36,000 m
Change in time = 74 s
a) Acceleration:
Acceleration (a) = (Change in velocity) / (Change in time)
Acceleration (a) = 36,000 m / 74 s
To get the acceleration in m/s², divide the distance by the time:
a ≈ 486.49 m/s²
b) To calculate the speed of the shuttle in km/h after 74 seconds, we need to use the formula:
Speed = Initial speed + (Acceleration x Time)
Given that the initial speed is not provided, we assume the shuttle starts from rest (0 km/h).
Initial speed = 0 km/h
Using the acceleration calculated in part a (486.49 m/s²) and the time of 74 seconds:
Time = 74 s
First, we need to convert acceleration from meters per second squared (m/s²) to kilometers per hour squared (km/h²):
Acceleration = 486.49 m/s²
Acceleration = 486.49 * (3600/1000)^2 km/h²
Acceleration ≈ 486.49 * 12.96 km/h²
Acceleration ≈ 6309.01704 km/h²
Next, we substitute the values into the formula:
Speed = Initial speed + (Acceleration x Time)
Speed = 0 km/h + (6309.01704 km/h² x 74 s)
To get the speed of the shuttle in km/h, multiply the acceleration by the time and add it to the initial speed:
Speed ≈ 0 + (6309.01704 km/h² x 74)
Speed ≈ 466,236.261 km/h
Therefore, the speed of the shuttle in km/h after 74 seconds is approximately 466,236.261 km/h.